We continued our lecture on Probabilities.<\/p>\n
We introduced the important concepts of dependant events and independant events. Dependant event is a group of outcomes where the outcomes depend on each other, while an independant event is a group of outcomes where the outcomes do not depend on each other.<\/p>\n
If A and B are two independant events, then the probability of A and B happening is:<\/p>\n
P(A and B) = P(A) * P(B)<\/p>\n
If A and B are two dependant events, then the probability of A and B happening is:<\/p>\n
P( A and B) = P(A) * P(B after A)<\/p>\n
Important to note is that for dependant events, when A happens, it changes the outcome space so P(B after A) is no longer the same as P(B), that is, we need to take into consideration about A’s happening.<\/p>\n
We further talk about the two importance concepts of Permutations and Combinations.<\/p>\n
A Combination is a group of outcomes where the order does not matter. For example, mixing two kinds of paints taken from 4 possible paints. Because of fixing effect, picking Red first then Blue has the same result of picking Blue first then Red. So here the order of picking does not matter.<\/p>\n
A Permutation is an arrangement of outcomes in which the order does matter. For example, picking two paints out of 4 possible pains with one paint for the background and the other paint for the design. Order here matters.<\/p>\n
We introduced that concept of factorial of a natural number where it is the product of itself and all the natural numbers less than it. So 5! = 5*4*3*2*1. And in particular, we define 0! = 1.<\/p>\n
With that we have the formulae to calculate number of permutations of taking r things out of possible n things as:<\/p>\n
nPr = n! \/ (n-r)!<\/p>\n
And the number of combinations of taking r things out of possible n things is:<\/p>\n
nCr = n! \/ [(n – r)! * r!]<\/p>\n
Homework is as follows:<\/p>\n